ABSTRACT: Critics of Microsoft and Google's dominance claim these companies are nothing but "giants standing on the shoulders of babies,"whose dominance destroys the incentives for entrants to innovate. By contrast, pro-Microsoft and pro-Google analysts stress the benefits of large, innovative firms. We analyze the validity of these competing claims in a model of R&D and product market competition between a dominant firm and a small rival. An increase in firm dominance, which we measure by a premium in consumer valuation, increases the dominant firm's incentives but decreases the rival firm's incentives for R&D. We provide sufficient conditions such that the positive effect on the dominant firm is mostly infra-marginal, whereas the negative effect on the rival firm is mostly marginal. As a result, the R&D encouragement effect is lower than the R&D discouragement effect; and if innovation is sufficiently important then firm dominance also decreases consumer and social surplus. We also provide conditions such that an increase in firm dominance increases the probability of innovation, essentially because the transfer of innovation incentives form the rival firm to the dominant firm reduces the probability of duplicative R&D efforts.